if the pH of a 0.14 aqueous solution of a weak base in 9.9, estimate the Kb of the base



To estimate the \( K_b \) of a weak base from its concentration and pH, we can follow these steps:

1. **Calculate the concentration of hydroxide ions \([OH^-]\)**:
   - First, find the pOH from the pH:
     \[
     pOH = 14 - pH = 14 - 9.9 = 4.1
     \]
   - Now, calculate the concentration of hydroxide ions using:
     \[
     [OH^-] = 10^{-pOH} = 10^{-4.1} \approx 7.94 \times 10^{-5} \, \text{M}
     \]

2. **Use the equilibrium expression** for the weak base dissociation:
   - The dissociation of a weak base \( B \) can be represented as:
     \[
     B + H_2O \rightleftharpoons BH^+ + OH^-
     \]
   - At equilibrium, if \( x \) is the concentration of \( OH^- \) produced, then:
     - \([BH^+] = [OH^-] = x\)
     - \([B] = [B]_0 - x = 0.14 - x\)

3. **Set up the \( K_b \) expression**:
   \[
   K_b = \frac{[BH^+][OH^-]}{[B]}
   \]
   Substituting in our values:
   \[
   K_b = \frac{(7.94 \times 10^{-5})(7.94 \times 10^{-5})}{0.14 - 7.94 \times 10^{-5}} \approx \frac{(7.94 \times 10^{-5})^2}{0.14}
   \]

4. **Calculate \( K_b \)**:
   \[
   K_b \approx \frac{(7.94 \times 10^{-5})^2}{0.14} \approx \frac{6.30 \times 10^{-9}}{0.14} \approx 4.50 \times 10^{-8}
   \]

Thus, the estimated \( K_b \) of the weak base is approximately \( 4.50 \times 10^{-8} \).

Would you like to go over any details or have any questions? Here are some related questions you might find interesting:

1. How would the \( K_b \) change if the concentration of the base was doubled?
2. What would the pH be if the solution were a strong base instead?
3. How can you experimentally determine the \( K_b \) of a weak base?
4. What is the relationship between \( K_a \) and \( K_b \) for conjugate acid-base pairs?
5. How does temperature affect the \( K_b \) of a weak base? 

Tip: Always ensure to check the units in your calculations to avoid errors.

if the pH of a 0.14 aqueous solution of a weak base is 9.9, estimate the Kb of the base

Learn how to estimate the Kb of a weak base from its concentration and pH. This solution explains the calculation of hydroxide ion concentration and the equilibrium expression for weak base dissociation. Suitable for advanced chemistry students.

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